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An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

A cryptographic hash function is most commonly one of the following: a one-way hash function, a collision-free hash function, a trapdoor one-way hash function, or a function ...

Fano's geometry is a finite geometry attributed to Fano from around the year 1892. This geometry comes with five axioms, namely: 1. There exists at least one line. 2. Every ...

A multistable polyhedron is a polyhedron that can change form from one stable configuration to another with only a slight transient nondestructive elastic stretch (Goldberg ...

A stereogram made of two pictures, one red and one blue, taken from offset positions. When the pictures are viewed through glasses with one lens of each color, the picture ...

Let f:R×R->R be a one-parameter family of C^3 maps satisfying f(0,0) = 0 (1) [(partialf)/(partialx)]_(mu=0,x=0) = -1 (2) [(partial^2f)/(partialx^2)]_(mu=0,x=0) < 0 (3) ...

Possessing more than one mode. A set of values having a single unique mode is said to be unimodal, one with two modes is called bimodal, and one with three modes is called ...

An analytic function f on the unit disk is called schlicht if 1. f is one-to-one, 2. f(0)=0, and 3. f^'(0)=1, in which case it is written f in S. Schlicht functions have ...

The Japanese variant of the game of chess. Shogi is played on a 9×9 uncheckered board, and each player begins with 20 pieces: one king, one rook, one bishop, two gold ...